Fibonacci

A number pattern from 800 years ago

In 1202, an Italian math teacher called Leonardo of Pisa, nicknamed Fibonacci, wrote a book that included this pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Each number is the two before it added up: 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, and so on. He didn't invent it. Mathematicians in India had written about it hundreds of years earlier. But his name stuck.

Divide one number by the next one, and as the numbers get bigger, you get closer and closer to 0.618. For example, 34 ÷ 55 = 0.618. Divide by the number two steps ahead, and you get about 0.382 (21 ÷ 55 = 0.382). Traders turn these into percentages: 61.8% and 38.2%.

Fibonacci retracements

A retracement is a pullback: price moves back part of the way it just came. Fibonacci levels are lines traders draw to guess how far a pullback might go before the trend maybe carries on. The three most watched:

• 38.2%: a shallow pullback.
• 50%: halfway back. This one isn't really a Fibonacci ratio, but traders watch it anyway.
• 61.8%: a deep pullback.

Work one out

Price climbs from $100 to $200. The move is 200 - 100 = $100. Now it starts to pull back. Measure down from the top:

• 38.2% of $100 is $38.20, so the level is 200 - 38.20 = $161.80
• 50% of $100 is $50, so the level is 200 - 50 = $150
• 61.8% of $100 is $61.80, so the level is 200 - 61.80 = $138.20

In the drawing, price pulls back to around the 50% line, pauses, then climbs again. Your app does this math for you: you click the bottom of the move, then the top, and it draws the lines.

Why they sometimes work

There's nothing magic about 61.8% in markets. Here are the honest reasons the levels sometimes seem to matter:

1. Lots of people watch them. If many traders are waiting to buy near the 61.8% line, their buying can make price bounce there. That's a self-fulfilling effect.
2. Pullbacks have to stop somewhere. With three lines fairly close together, price will stop near one of them pretty often just by chance. Then it looks like the lines "worked."
3. They line up with other things. A Fibonacci level gets more attention when it lands on an old support level or a moving average.

Where it fails

• Two traders can pick different starting and ending points and get different lines. Which high? Which low?
• Price often slices straight through all three levels.
• After the fact, it's easy to notice the level that "worked" and forget all the ones that didn't. There's no strong proof that these exact numbers are special. Treat them as zones to watch, not walls.

Remember

• In the Fibonacci pattern, each number is the two before it added up.
• Traders watch the 38.2%, 50% and 61.8% pullback levels.
• If price rises from $100 to $200, the levels are $161.80, $150 and $138.20.
• They sometimes work mostly because many traders watch them. They're zones, not walls.